I would like to generate a particle star field that I could keep as static background
I have gotten a static field but the mesh is in the way and I cannot see through the object, ...


To hide the emitter uncheck the Emitter option in the render panel:


Unfortunatley it is not possible to fully freeze the physic simulation. The minimum timestep is 0.001/frame.

If you're using objects for your particles you can press CTRLSHIFTA or search Make Duplicates Real from the search menu (SPACE in the viewport) to create static duplicates.

If you're not using objects you could still 


Create an object with a single vertex at (0.0,0.0,0.0) and use it for the particles.
Duplicate these vertices with CTRLSHIFTA
Apply a halo material to the single vertex object and remove the particle system.


To simpify this, you may use this script

import bpy
#creates a mesh object
#from the selected particle system
#from the current frame

obj=bpy.context.active_object

ps=obj.particle_systems[0]

count=0
for pl in ps.particles:
    if pl.alive_state=='ALIVE':
        count+=1

mesh=bpy.data.meshes.new('point_cloud')
mesh.vertices.add(count)

for i in range(count):
    mesh.vertices[i].co=ps.particles[i].location

dupli=bpy.data.objects.new('point_cloud',mesh)
bpy.context.scene.objects.link(dupli)


You could also write the cache to disk by enabling the option Disk Cache in the Cache panel and baking the simulation afterwards. With the default options a folder named blendcache_blendname will be created in the folder where the .blend-file is located. 

In this folder the data for each frame is stored. The template/scheme is filename_frame_subframe. Just copy your frame you want to be frozen and replace the following frames. The amount of particles should be constant in this time period. No particle should be born or die.

Afterwards enable the External option and choose blendcache_blendname as folder and filename as filename.